Abstract

The microstructure of granular materials is the main factor determining their macroscopic behaviour. We study systematically the statistical characteristics of volume elements (called quadrons) of microstructures of mono-and polydisperse planar disc packs granular and report a number of new results. The packs analysed were of different intergranular friction coefficients, μ, contained about 20,000 discs each and were brought to mechanical equilibrium under identical isotropic compression stresses from three different initial states: loose, intermediate and dense. Our findings are the following. (i) The rattlers volume fraction φr is not affected by the disc size distribution (DSD). (ii) Excluding the rattlers, we find that the relation between the packing fraction φ′ and the mean coordination number ̄z is independent of the initial state. Together with result (i), this allows us to separate the effects of the DSD and the initial state on the microstructure. (iii) We relate analytically ̄z, φ′ and the (normalised) mean quadron volume ̄ν′. (iv) Combining (iii) and a relation between ̄z and the mean cell order, ē, derived from Euler's topological relation, we show that (ii) is a result of the geometrical relation between ̄ν′ and ē. (v) The probability density function of the quadron volumes, normalised by ̄ν′, is universal for all the studied systems and it can be fit reasonably well by a Γ distribution.